A British exit from the European Union would plunge the two parties into a messy divorce and force them build a new relationship after a long marriage.
Here are the next steps in a complicated process that Brussels and London would have to negotiate if Britons vote for a "Brexit" in the June 23 referendum.
Whatever the result, there will be a special meeting in Brussels on June 24 at 10:30 am (0830 GMT) of the EU`s top officials -- EU President Donald Tusk, European Commission chief Jean-Claude Juncker, European Parliament head Martin Schulz and Netherlands Prime Minister Mark Rutte, whose country holds the six-month EU presidency.
A full EU summit of all 28 national leaders is already scheduled for the following week on June 28-29.
But in the event of a "Brexit" vote, key EU leaders like German Chancellor Angela Merkel and French President Francois Hollande are likely to hold emergency talks before that.
There is also likely to be an emergency session of the European Parliament before the summit.
British Prime Minister David Cameron has said if the country votes to leave, he will "straight away" trigger Article 50 of the EU`s 2009 Lisbon Treaty, which governs how a country can leave the bloc.
Article 50 says that "any member state may decide to withdraw from the Union in accordance with its own constitutional requirements" and sets out the procedure to do so.
But if Cameron finds himself forced out of a job, then a new government of "Brexiteers" is reportedly looking at postponing triggering Article 50 to secure a better deal.
EU law stipulates a two-year time period for dissolving all contractual ties under Article 50 before a state officially leaves the bloc.
But negotiations on a new relationship and trade deals between a newly-independent London and Brussels could take a lot longer.
Tusk has warned that getting approval from each one of the remaining 27 member states, plus the European Parliament, could take a further five years -- making seven years in all.
The British government warned in a report in February that it could take up to 10 years to tie up all the loose ends.
The pro-Brexit camp says it would aim to fast track negotiations and quit the EU by the end of 2019.
Cabinet Minister Chris Grayling, who backs leaving the EU, told the Financial Times that Britain would also pass laws to restrict the free movement of EU citizens before it actually leaves the bloc.
Brussels is reportedly considering measures to suspend Britain from the EU`s single market if it takes such a step.
The simplest and most frequently cited option is for Britain to join Iceland and Norway as members of the European Economic Area, which would give them access to the single market.
That however would mean London still having to obey the EU`s rules despite no longer having any say in how they are formed, plus still having to pay money to Brussels.
The Swiss model is another popular one for pro-Brexit campaigners but it is "not likely that Britain would take this route", said Jean-Claude Piris, a former senior EU jurist who is now a consultant.
Piris pointed out that Switzerland has had to sign hundreds of trade agreements with the EU and that Brussels is still not satisfied with the relationship.
Other options include a free trade deal with the EU or a customs union similar to that between Turkey and the EU. Failing that, it would simply become a trading partner like the United States or China.
Whatever happened, Britain would end up a "sort of satellite to the EU", said Piris.
London would have to negotiate the status of the two million Britons living or working in the EU.
This would particularly affect their pensions and rights to healthcare, with the British government noting: "UK citizens resident abroad, among them those who have retired to Spain, would not be able to assume that these rights will be guaranteed."